I'm not sure if you are still looking for an answer, but here it is:
I haven't tried those specific methods, but I have installed Windows 10 on an external hard drive. It should be the same, although you will need a Windows 7 iso image.
Step 1: Download a virtual machine to run Windows on. I used VMWare Fusion and used a 30-day trial.
Step 2: Search "windows 10 iso image" and click the first link from Microsoft. Download it.
Step 3: Open the VMWare application and upload the Windows 10 iso image onto it, and run Windows.
Step 4: Go on your virtual Windows and download WinToUSB from this: https://www.easyuefi.com/wintousb/.
Step 5: Find and download a Windows 7 iso image. The official Microsoft website has it, but you will need the product key you received when you first installed windows.
Step 6: Open the WinToUSB tool and upload the .iso image onto it, and choose which version to install. Connect your external drive to your Mac, make sure it connects to VMWare, and select it once it shows up on WinToUSB.
Step 7: Wait until the tool installs Windows 7 onto the external drive. While this is running, go to the Bootcamp app and ONLY download the Windows Support Software.
Step 8: Once the WinToUSB tool finishes installing, you can close out of VMWare by shutting down from the virtual Windows. The connected external drive should show up on your mac again, and drag the Windows Support Software folder into the drive.
You should now have an external drive with Windows 7 on it, and the Windows Support Software on it as well. You can boot from it by restarting and holding
option and choosing the external drive. Use the Windows Support Software to install the correct Apple Drivers in the external drive when inside the Windows 7 boot.
This was the method that worked for me on an Early 2014 MacBook Air on High Sierra.